Place sweetbreads with water to cover in a medium mixing bowl. Soak for 1 hour. Drain well; remove and discard white membrane.
Combine drained sweetbreads, 2 quarts water, vinegar, and 2 teaspoons salt in a large Dutch oven. Bring mixture to a boil. Reduce heat; cover and simmer 20 minutes.
Remove sweetbreads, and cut into serving-size pieces. Combine egg and 2 tablespoons water in a small bowl; set aside. Combine breadcrumbs, remaining salt, and pepper in a small bowl; set aside. Dip sweetbreads in egg mixture; roll in breadcrumb mixture
Melt lard in a large skillet over medium heat. Add sweetbreads; cook over low heat 10 minutes or until browned, turning to brown all sides. Remove sweetbreads; drain.
Cook peas in a medium saucepan over medium heat until hot. Drain and add butter.
Serve peas in a small bowl on a platter. Place sweetbreads around bowl on platter; garnish with parsley. Serve immediately.